Question

Relative density of a body with respect to a medium of density ${\rho _1}$ is a. What is the relative density of a body with respect to a medium of density ${\rho _2}$ ?
A. $\dfrac{{a{\rho _2}}}{{{\rho _1}}}$
B. $\dfrac{{a{\rho _1}}}{{{\rho _2}}}$
C. $\dfrac{{{\rho _1}}}{{a{\rho _2}}}$
D. $\dfrac{{{\rho _2}}}{{a{\rho _1}}}$

Answer 1

In order to solve this question we need to understand specific gravity. Specific gravity is defined as ratio of density of substance to the density of reference object, for example specific gravity of a molecule in crystal is defined as ratio of density of molecule to the density of crystal. This density is also known as relative density of objects. Inside fluid, if an object is dipped in it then the relative density is defined as ratio of density of object to the density of liquid or fluid.

Complete step by step answer:
Given in question, density of medium one is, ${\rho _1}$ and density of medium two is, ${\rho _2}$.Relative density of object in medium one is, $a$.Let the density of object is $\rho$ and also let the relative density of object in medium two be, $r$.Since we know,
$R = \dfrac{{{D_O}}}{{{D_R}}}$
Here, $R$ is relative density, ${D_O}$ is density of object kept in medium and ${D_R}$ is the density of reference medium in which object is kept.

Then for medium one we have, $R = \dfrac{\rho }{{{\rho _1}}}$
$a = \dfrac{\rho }{{{\rho _1}}}$
So density of object is, $\rho = a{\rho _1} \to (i)$
Now for medium two we have, $r = \dfrac{\rho }{{{\rho _2}}}$
Putting value of density of object from (i) we get,
$\therefore r = \dfrac{{a\;{\rho _1}}}{{{\rho _2}}}$

So the correct option is B.

Note: It should be remembered that relative density or specific gravity can be measured by an acid hydrometer which proved to be very helpful in automobiles. Hydrometer is based on principle of Archimedes Principle, which states that if any object pressed in liquid with a force then water exerts an upward buoyant force on the object which is proportional to the amount of liquid it displaced.